Finally, to capture non-Gaussian effects of the statistics, as displayed, e.g. in Fig. REF , we use for example Lévy-stable distributions [1]} as discussed in [2]}. These distributions are characterized by their scale parameter \(\sigma _S\) , similar to a standard deviation, and their stability parameter \(\alpha _S\)  that gives the tails of the distribution. Stable distributions with \(\alpha _S=2\)  are Gaussian distributions while \(\alpha _S<2\)  indicates heavy tails. For the full 2017 data, we found that \(\alpha _S \approx 1.9\) , i.e. well below \(\alpha _S=2\) .
Analogue to the Gaussian approach, we may now formulate a generalized Fokker-Planck equation [2]}, [4]} to obtain the probability distribution of the angular velocity \(\omega \) .
We require that the noise at each node in the system follows a stable distribution with one stability parameter \(\alpha _{S}\)  but arbitrary scale parameter, which we set as \(\sqrt{2} \sigma _{S,i}^{P}\) , where the square root of 2 is necessary to resemble Gaussian results for \(\alpha _S=2\) . Then, the resulting distribution of the angular velocity is also a stable distribution, with stability parameter \(\alpha _S\)  and scale parameter given as [2]}
\(\bar{\sigma }_{S}^{\omega }=\frac{1}{\sqrt{2}\sum _{i=1}^{N}M_{i}}\left[\frac{1}{\gamma \alpha _{S}}\sum _{i=1}^{N}\left(\sigma _{S,i}^{P}\right)^{\alpha _{S}}\right]^{1/\alpha _{S}}.\) 
